A353639 a(n) = 1 if n is odd and A064989(sigma(n)) > A064989(n), otherwise 0. Here A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

For n > 1, a(n) = A000035(n) * (1-A348737(A064989(n))) = A000035(n) - A353638(n). [Conjectured, see comments in A336702]

Prog

(PARI)
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353639(n) = ((n%2) && (A064989(sigma(n))>A064989(n)));

Crossrefs

Characteristic function of A348749 (see also A348739).

Cf. A000035, A000203, A064989, A336702, A348737, A353638.

Sequence in context: A369640 A037816 A297038 * A353569 A353477 A044939

Adjacent sequences: A353636 A353637 A353638 * A353640 A353641 A353642

Keyword

nonn

Author

Antti Karttunen, May 04 2022

Status

approved